Find the harmonic conjugate of the point (5,2) w.r.t. points P(2,10) and Q(6,-2).
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Let (5,2) divide the join of (2,10) and (6,-2) in the ratio k:lk(6)+1(2)k+1=5 ;k(-2)+1(10)k+1=2Any one of the above equality is enough to find k.6k+2k+1=56k+2=5k+5k=3The ratio is 3:1Harmonic conjugate is given bykx2-lx1k-l,ky-ly1k-lHere k=3,l=1,x1,y1=2,10 and x2,y2=6,-2Harmonic conjugate=36-123-1,3-2-1103-1=18-22,-6-102=8,-8
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